Write an equation in point-slope form of the line that passas through the point (-6,6) and has a slope of m=3/2

Answer:

2,4 3,5

Step-by-step explanation:

Answer:

1019

Step-by-step explanation:

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Step-by-step explanation:

The formula for finding the volume of a rectangular prism:

\(V=L (base) \times W \times H\)

Multiply all sides.

To solve:

Multiply 11.6, 13.1, and 18.2

\(V=11.6 \times 13.1 \times 18.2\)

Multiply:

\(V=11.6 \times 13.1 \times 18.2\)

\(V=151.96 \times 18.2\)

\(V=2765.672\)

The volume equals 2765.672in^3

Rounded: 2765.67in^3

Solution:

Note that:

Finding the volume of the prism:

The volume of the prism is 2765.672 in³

Answer:

3.5 miles per day

Step-by-step explanation:

There are 7 days in a week

24.5 miles in a week

24.5 / 7 days

3.5 miles per day

Answer:

3.4 miles

Step-by-step explanation:

You would divide 24.5 by 7 since there are 7 days in a week giving you a quotient of 3.5

Answer:

D. \((5,6)\)

Step-by-step explanation:

Let \(R(x,y) = (1,2)\), we proceed to perform all operations described on statement:

1) Dilation

\(R'(x,y) = O(x,y) + k\cdot [R(x,y)-O(x,y)]\)  (1)

Where:

\(O(x,y)\) - Point of reference.

\(R(x,y)\) - Original point.

\(R'(x,y)\) - Dilated point.

\(k\) - Scale factor.

If we know that \(O(x,y) = (0,0)\), \(R(x,y) = (1,2)\) and \(k = 3\), then the dilated point is:

\(R'(x,y) = (0,0) +3\cdot [(1,2)-(0,0)]\)

\(R'(x,y) = (0,0) +3\cdot (1,2)\)

\(R'(x,y) = (3,6)\)

2) Translation

\(R''(x,y) = R'(x,y) + T(x,y)\) (2)

Where:

\(R'(x,y)\) - Original point.

\(T(x,y)\) - Translation point.

\(R''(x,y)\) - Translated point.

If we know that \(R'(x,y) = (3,6)\) and \(T(x,y) = (2,0)\), then the translated vector is:

\(R''(x,y) = (3,6)+(2,0)\)

\(R''(x,y) = (5,6)\)

Therefore, the correct answer is D.

Answer:d

Step-by-step explanation:

The circumference of the circle is 62.8cm.

The Circumference of the circle is given by the formula,

Circumference = 2*\(\pi\)*r cm.........equation 1

Given, r = 10cm

On substituting the radius value in equation 1

Circumference = 2*\(\pi\)*10

Circumference = 62.8 cm

Therefore, the circumference of the circle is 62.8cm.

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Answer:

n = -1/3

Step-by-step explanation:

let 'n' = a number

2n + 7 = 5 - 4n

6n + 7 = 5

6n = -2

n = -1/3

Check the picture below, so Francesca's throw looks more or less like that, and it hits the ground when h(t) = 0

\(\stackrel{h}{0}=1+14t-5t^2\implies 5t^2-14t-1=0 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{5}t^2\stackrel{\stackrel{b}{\downarrow }}{-14}t\stackrel{\stackrel{c}{\downarrow }}{-1}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}\)

\(t= \cfrac{ - (-14) \pm \sqrt { (-14)^2 -4(5)(-1)}}{2(5)} \implies t = \cfrac{ 14 \pm \sqrt { 196 +20}}{ 10 } \\\\\\ t= \cfrac{ 14 \pm \sqrt { 216 }}{ 10 }\implies t=\cfrac{ 14 \pm 6\sqrt { 6 }}{ 10 }\implies t=\cfrac{ 7 \pm 3\sqrt { 6 }}{ 5 }\implies t\approx \begin{cases} ~~ 2.870~\checkmark\\ -0.070 \end{cases}\)

so there are two valid values, however we can't use the negative one, since the phenomena is for seconds and we can't have negative seconds in this case.

Answer:

150

Step-by-step explanation:

The sum of the angles of a quadrilateral are 360.  Let x be the unknown angle

30+70+110+x = 360

Combine like terms

210 +x = 360

Subtract 210 from each side

210+x-210 = 360-210

x = 150

Answer:

The measures of the fourth angle is 150 .

Step-by-step explanation:

The measures of three angles of quadrilateral are 30 , 70 and 110.

Find the measures of fourth angle.

Let, the measures of fourth angle be x.

We know that sum angles of quadrilateral are 360 .

30 + 70 + 110 + x = 360

combine like terms

210 + x = 360

subtract 210 from 360.

x = 360 - 210

x = 150

Therefore, the fourth angle of quadrilateral is 150.

Answer:

=1

Step-by-step explanation:

log3(x+2)-log3(x)=1

Subtraction sign means you can divide the values inside the parintheses

log3(x+2/x)=1

split up the fraction into x/x and 2/x; x/x = 1

log3(1+(2/x))=1

Change of base - three to the first power = value in parintheses

3to1st=1+(2/x)

subtract 1 from both sides

2=2/x

divide both sides by 2

x=1

;)

Answer:

6720 ways different

Step-by-step explanation:

In this case, we must calculate the different ways using the permutation formula:

nPr = n! / (n - r)!

where n is the total number of people and r would come being the group of person that you want to put together the groups, therefore n = 8 and r = 5

replacing:

8P5 = 8! / (8 - 5)!

8P5 = 6720

That is to say that there are 6720 ways different winning groups are possible

Explanation

Step 1

Multiply equation(1) by -1 and add the result to equation(2)

The power series of the given function  is 1 + (2x) + (2x)² + (2x)³+ --------------------- + (2x)ⁿ

We know very well that sum of n terms who are in geometric progression their sum of expression is given by  a/1-r where a is first term and r is common ratio between the terms.

Now, we have function f(x)=[1 / (1-2x)]

On comparing with a/1-r with f(x),we get

=>a=1 and r=2x

Now, we know that first term of geometric progression is given by =1

second term of geometric progression is given by=a × r= 1 ×2x

third term of geometric progression is given by =a×r² =1×(2x)²

fourth term of geometric progression is given by=a×r³ =1 × (2x)³

nth term of geometric progression is given by =a×(r)ⁿ = 1 × (2x)ⁿ

Therefore, according to the given formula progression series of given function is=a+ ar +ar² + ar³ + -----------arⁿ

=>progression series = 1+ 2x + (2x)² + (2x)³ + --------- + (2x)ⁿ.

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The algebraic expression (3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) can be simplified to give 3x/(x - 3) which makes the option D correct.

Simplification of an algebraic expressions is the process of writing an expression in the most efficient and compact way, that is in their simplest form, without changing the value of the original expression.

Simplifying the algebraic expression we have:

(3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4)

by factorization;

3x² - 6x = 3x(x - 2)

x² - 6x + 9 = (x - 3)(x - 3)

x² - x - 6 = (x - 3)(x + 2)

x² - 4 = (x + 2)(x - 2)

(3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) = 3x(x - 2)/(x - 3)(x - 3) × (x - 3)(x + 2)/(x + 2)(x - 2)

cancel out common factors we have;

(3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) = 3x/(x - 3)

Therefore, the algebraic expression (3x² - 6x)/(x² - 6x + 9) × (x² - x - 6)/(x² - 4) can be simplified to give 3x/(x - 3)

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The surface area of the given sphere is 764.15 square inches.

Given that, the sphere has diameter = 15.6 inches.

Here, radius = 15.6/2 = 7.8 inches

We know that, surface area of a sphere is 4πr².

Now, surface area = 4×3.14×7.8²

= 764.15 square inches

Therefore, the surface area of the given sphere is 764.15 square inches.

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f(x) = x^3 - x^2 , over the interval (-1,2)

So, the rate of change will be as following:

at first, we will find f(2) and f(-1)

f(2) = 2^3 - 2^2 = 8 - 4 = 4

f(-1) = (-1)^3 - (-1)^2 = -1 - 1 = -2

So, the rate of change:

The volume V(x) in cubic inches of the open-top box is (15\(x^{2}\) - 2\(x^{3}\))

and side of length x in inches of the square cutouts is

V(1) = 15 - 2 = 13

x ∠ 7.5

The vertical sides were 15 inches before we cut out the corners.  

The horizontal sides were 15 inches before we cut out the corners.

So now, if you fold all of the "tabs" up, you get a box that has a height of "x".  

The sides are now each missing a length of "x" from each end.  

So the longer edges of the box are now (15 - 2x) long.  

The shorter edges of the box are now (15 - 2x)

The volume of a box is given by V = (length)(width)(height)

 length = 15 - 2x

width and height of the box are equal to x in so

Multiply these together and get:

V(x) = (15 - 2x)(x)(x)

V (x)  =  (15\(x^{2}\) - 2\(x^{3}\))

let x = 1

V (x) =  (15\(x^{2}\) - 2\(x^{3}\))

V(1) = 15 - 2 = 13

First x must be greater than 0,

then, we have 2x ∠ 15

                          x ∠ 7.5

therefore, The volume V(x) in cubic inches of the open-top box is (15\(x^{2}\) - 2\(x^{3}\))

side of length x in inches of the square cutouts is

V(1) = 15 - 2 = 13

x ∠ 7.5

This unit has two parts:

The surface area of a box, and its volume

The length of the diagonal of a box

Each student should bring an empty cereal box (or some other box) to work on. (The length, width, and height of the box should all be different.)

Formula for the area of the surface

(a) If l, w, and h are the length, width, and height of a box, its surface area is given by surface area = 2*(l*w + l*h + w*h). (Do you see it?)

(b) Measurements

Measurements are made in inches and sixteenths of an inch, but they are recorded as decimals.

1/8 inch = .125 inch, ¼ inch = .25 inch, 3/8 inch = .375 inch, ½ inch = .5 inch, and so on.

Example:

length l = 8.375 inches

width w = 6.125 inches

height = 2.25 inches

(c) How to enter these measurements into a TI-108 calculator to get the surface area:

8.375*6.125 M+       51.29…

8.375*2.25 M+         18.84…

6.125*2.25 M+         13.78…

MRC * 2 =                167.84… square inches

We round this to 168 square inches (more or less)

Part 1b. We can also find the volume of the box:

volume = l*w*h = 8.375*6.125*2.25 = 115.4… cubic inches

If this were a hands-on unit, we would paper the box with square inch paper and fill the box with cubic inch blocks to see whether our computations are confirmed.

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Answer:

38

38 38 38 38 38 38 38 38okay so all you're going to do 4 * 3 + 4 * 4 what is going to give you 12 +16

Hello

2/7 = 2x5/7x5 = 10/35

10/35 > 6/35

=> 2/7 > 6/35

Answer:

5

Step-by-step explanation:

(+3)+(+2) = 3+2 = 5.

Answer:

5

Step-by-step explanation:

(+3)+(+2)

Add 3 and 2 to get 5.

5

The amount remaining after 50 years is approximately 45.5% of the Initial amount, A₀.

The given exponential function represents the amount A(t) (in grams) of cesium-137 remaining after t years:

A(t) = A₀ * (1/2)^(t/30)

We are asked to find the initial amount A₀ and the amount remaining after 50 years.

1. Initial amount:

The initial amount, A₀, is the amount of cesium-137 present at t = 0 years. To find A₀, we substitute t = 0 into the equation:

A(0) = A₀ * (1/2)^(0/30)

A(0) = A₀ * 1

Since anything raised to the power of zero is 1, we have A(0) = A₀ * 1, which simplifies to A(0) = A₀.

Therefore, the initial amount of the sample is A₀.

2. Amount after 50 years:

To find the amount remaining after 50 years, we substitute t = 50 into the equation:

A(50) = A₀ * (1/2)^(50/30)

Now we can calculate the amount using the given formula:

A(50) = A₀ * (1/2)^(5/3)

To round the answer to the nearest gram, we evaluate the expression and round the result to the nearest gram:

A(50) = A₀ * 0.455

A(50) ≈ A₀ * 0.455

Therefore, the amount remaining after 50 years is approximately 45.5% of the initial amount, A₀.

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\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely to }x^2}{y=\cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} y=5\\ x=3 \end{cases} \\\\\\ 5=\cfrac{k}{(3)^2}\implies 5=\cfrac{k}{9}\implies 45=k\hspace{5em}\boxed{y=\cfrac{45}{x^2}} \\\\\\ when~y=1\frac{4}{5}\textit{ what is "x"?}\implies 1\frac{4}{5}=\cfrac{45}{x^2}\implies \cfrac{9}{5}=\cfrac{45}{x^2} \implies 9x^2=(5)(45) \\\\\\ x^2=\cfrac{(5)(45)}{9}\implies x^2=25\implies x=\sqrt{25}\implies {\Large \begin{array}{llll} x=5 \end{array}}\)

Unit analysis is a tool that we can use to convert units. It involves multiplying the original number by a fraction to cancel out units.

We're given:

\(\dfrac{3240\hspace{4}feet}{hour}\)

We also know that:

\(\dfrac{hour}{60\hspace{4}minutes}\)

Multiply the two to cancel out the hour:

\(\dfrac{3240\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{3240\hspace{4}feet}{60 minutes}\)

Simplify:

\(=\dfrac{54\hspace{4}feet}{minute}\)

\(\dfrac{54\hspace{4}feet}{minute}\)